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Published byCharlotte Campbell Modified over 9 years ago
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Regression Analysis with MATLAB
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MATLAB codes Read the data into workspace of MATLAB clear; data=xlsread('D:\UIC lectures\RA 2010\chap3\hospital manpower.xls');
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MATLAB codes
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Read the data into workspace of MATLAB y=data(:,3); x(:,2)=data(:,2); x(:,1)=1; n=size(x,1);
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MATLAB codes Read the data into workspace of MATLAB
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MATLAB codes Computation steps
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MATLAB codes Calculate Beta and Q beta=inv(x'*x)*x'*y; Q=(y-x*beta)'*(y-x*beta);
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MATLAB codes Calculate Beta and Q
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MATLAB codes Calculate H, yhat, sigma square and covariance of beta h=x*inv((x'*x))*x'; yhat=h*y; sigma2=Q/(n-2); covbeta=sigma2*inv(x'*x);
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MATLAB codes Calculate H, yhat, sigma square and covariance of beta
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MATLAB codes Calculate H, yhat, sigma square and covariance of beta
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MATLAB codes Define Dn yi=ones(n,1); i=eye(n); D=i-(1/n)*yi*yi';
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MATLAB codes Define Dn
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MATLAB codes Compute SStotal and SSreg SStotal=y'*D*y; SSreg=yhat'*D*yhat;
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MATLAB codes Compute SStotal and SSreg
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ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 Residual0.863 Total111.917
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ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917
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ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917 N=? Sigma square=? R square=?
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ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917 N=12 Sigma square= 0.0863 R square=0.550
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ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917 b1=? b0=? Var(b1)=? Var(b0)=? X bar=49.3333 Y bar=3.5 Sxx=306.67 Sxy=17.97
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ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917 b1=0.059 b0=0.003 Var(b1)= 0.000281 Var(b0)= 0.69208 X bar=49.3333 Ybar=3.5 Sxx=306.67 Sxy=17.97
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ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917 t(b1)=? X bar=49.3333 Ybar=3.5 Sxx=306.67 Sxy=17.97
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ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917 t=3.493 X bar=49.3333 Ybar=3.5 Sxx=306.67 Sxy=17.97
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ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917 Var(y-hat)=?, at x=45 X bar=49.3333 Ybar=3.5 Sxx=306.67 Sxy=17.97
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ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917 Var(y-hat)=0.012476, at x=45 X bar=49.3333 Ybar=3.5 Sxx=306.67 Sxy=17.97
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That’s all
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